Abstract The literature on mixed oligopoly shows that when production costs are quadratic the public firm is privatized if the competition in the product market is high enough. Similarly, when the public firm is less efficient than private firms and the marginal costs of production are constant, the government privatizes the public firm if its efficiency is low enough. In this paper we analyze this issue assuming that the public firm maximizes the weighted sum of consumer surplus, private profit and the profit of the public firm. If all firms have the same marginal cost of production we obtain that for some value of parameters the government does not privatize the public firm regardless of how many private firms are competing in the product market. We also obtain that the consumer surplus can be lower in the mixed oligopoly than in the private oligopoly.